Street Party

Stage: 2 Challenge Level:

It is wonderful to receive solutions that show
so much thought and effort. Joanne has a really neat way of
thinking about patterns with start points for the routes. (Well
done!) Natasha has tried to report her work in an organised way and
come up with some good "What if...'' questions. Jenny has a nice
way of explaining her thinking. Jill tries to look at the
investigation in some different ways.

Solution 1, Joanne, West Flegg Middle School

I first thought about the simple routes, for example straight
down. That can be changed by going horizontally across the
middle.

Then I worked on harder routes. I fund that all regular routes
had 4 starting points around the road pattern (without going back
over the same route). The irregular pattern of routes had 8
starting points around the road pattern.

In finding this out, I have found out the number of times each
route can be used.

The set of road patterns are as follows:
(each map shows one route and all its starting points)

Solution 2, Natasha, West Flegg Middle School

I am finding the routes by picking a square and then just
doodling until I find a route that is split into halves (8). Also,
by doing the opposite to the one I had done before. I am also
drawing a very faint line horizontally - and vertically in pencil,
so that I can see roughly where I have to split the street into
two. So really what I had to do was divide 16 by 2 = 8.

I had this sudden thought that what if I worked out how many
ways I could divide 16 and then I thought maybe I could then prove
that I had found them all. But as you can see below, that was
definitely not going to work because I only found 2 ways.

This is as far as I got until I moved on

My suggestions for "What if''

What would happen if two houses didn't approve of a street
party, therefore you wouldn't be able to split the houses (build a
fence there?)

What would happen if someone from the street were on holiday and
they were coming back on the night of the party and you didn't want
to build a fence because you didn't know how they would react.

What would happen if you had 49 houses to try and split
equally?

What you would have to do is split the 49 houses into 2 24s that
would make 48, then you would have to share the house left over so
that you could have 6 hours there each (half of 12 which is the
night), or if you were counting it by the whole day (24 hours) 1
street party would use that house 1/4 of the way through the day
and have 6 hours and the other party would start 3/4 of the way
through.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.